High temperature interactions between magmas and volatile-rich sedimentary rocks, usually referred as assimilation, may have variable consequences for magmatic processes depending on the nature of the sedimentary rocks. This manuscript reviews the assimilation mechanisms for carbonate, evaporitic and carbonaceous rocks and the magmatic processes that are directly impacted by these interactions. A first, poorly studied consequence of magmatic assimilation, which is however potentially important, is on magma emplacement mechanism. The nature of the sedimentary rocks is likely to play a role in the formation and propagation of sill-like structures, therefore controlling magma intrusion in sedimentary basins. This in turn may favour the interaction of the magma with the sedimentary rocks that are more easily intruded. When the magma volume is high, as in the case of large igneous provinces, magmatic intrusion into sedimentary rocks may produce extensive degassing. The assimilation and, to a larger extent, the thermal metamorphism of volatile-rich sedimentary rocks may indeed cause significant gas release with noteworthy environmental consequences (e.g. greenhouse effect and mass extinction). At the scale of a single volcano, the addition of external volatiles due to magma-sediment interactions can enhance degassing and/or modify the eruptive behaviour. The effect of assimilation on the redox conditions of the magma and therefore on ore forming processes is also extremely important, although much less investigated. Significant modifications of the magma redox state can trigger the segregation/crystallization of magmatic phases that are generally uncommon or represent accessory phases (like native iron, sulfide melt or oxide minerals), possibly forming world class ores. Furthermore, magma-sediment interactions may produce magmatic-hydrothermal fluids enriched in metals and metalloids, but this field is almost unexplored. Least but not last, the assimilation of volatile-rich sedimentary rocks can modify the composition of the magma, significantly in some extreme cases and not only in terms of volatile content. Assimilation of carbonate rocks produces silica undersaturated, alkali-rich magmas, while the effect of carbonaceous and evaporitic rocks is almost uninvestigated. The manuscript deals with four rock types (carbonate, sulfate, chloride-bearing and carbonaceous rocks); case studies are presented for each rock type to illustrate how magma-sediment interactions affect the different magmatic processes.